Journal of Integer Sequences, Vol. 26 (2023), Article 23.6.2

Common Values of Generalized Fibonacci and Leonardo Sequences

Bibhu Prasad Tripathy and Bijan Kumar Patel
Department of Mathematics
School of Applied Sciences
KIIT University Bhubaneswar
Odisha 751024


For an integer k ≥ 2, let Fn(k) be the k-generalized Fibonacci sequence that starts n with 0,..., 0, 1, 1 (k terms) and each term afterwards is the sum of k preceding terms. In this paper, we find all the k-generalized Fibonacci numbers that are Leonardo numbers. More explicitly, we solve the Diophantine equation Fn(k) = Lem in positive integers n, k, m with k ≥ 2.

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(Concerned with sequences A000032 A000045 A001595.)

Received January 31 2023; revised versions received February 8 2023; May 17 2023; May 26 2023. Published in Journal of Integer Sequences, June 12 2023.

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